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The "nine dots" puzzle. The puzzle asks to link all nine dots using four straight lines or fewer, without lifting the pen. The nine dots puzzle is a mathematical puzzle whose task is to connect nine squarely arranged points with a pen by four (or fewer) straight lines without lifting the pen.
Like approximate entropy (ApEn), Sample entropy (SampEn) is a measure of complexity. [1] But it does not include self-similar patterns as ApEn does. For a given embedding dimension, tolerance and number of data points, SampEn is the negative natural logarithm of the probability that if two sets of simultaneous data points of length have distance < then two sets of simultaneous data points of ...
The most simple rectangle checking method lies in checking the borders of equally sized rectangles, resembling a grid pattern. (Mariani's algorithm.) [14] A faster and slightly more advanced variant is to first calculate a bigger box, say 25x25 pixels. If the entire box border has the same color, then just fill the box with the same color.
If, for example, there are two balls and three bins, then the number of ways of placing the balls is (+) = =. The table shows the six possible ways of distributing the two balls, the strings of stars and bars that represent them (with stars indicating balls and bars separating bins from one another), and the subsets that correspond to the strings.
Originally constructed as a curve, this is one of the basic examples of self-similar sets—that is, it is a mathematically generated pattern reproducible at any magnification or reduction. It is named after the Polish mathematician Wacław Sierpiński but appeared as a decorative pattern many centuries before the work of Sierpiński.
For example, the diagram below shows n = 20 and the partition 20 = 7 + 6 + 4 + 3. Let m be the number of elements in the smallest row of the diagram ( m = 3 in the above example). Let s be the number of elements in the rightmost 45 degree line of the diagram ( s = 2 dots in red above, since 7 − 1 = 6, but 6 − 1 > 4).
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Kawasaki's theorem or Kawasaki–Justin theorem is a theorem in the mathematics of paper folding that describes the crease patterns with a single vertex that may be folded to form a flat figure. It states that the pattern is flat-foldable if and only if alternatingly adding and subtracting the angles of consecutive folds around the vertex gives ...
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